Gian-Carlo Rota. I really wish I could pinpoint the moment that I came across some of his work, but I can't. And I've only just begun graduate work so it's impossible to be really honest about what sort of impact he has had on me... only time can tell.
But nonetheless, his writings are truly inspiring. It's tough to describe the wonder they have given me. Rota began as a functional analyst (PhD under Jacob Schwartz, of the Dunford & Schwartz fame) and moved over to algebraic combinatorics in the 1960s. One of his first papers that has stuck in my mind is "The Number of Partitions of a Set" in which he applies the techniques of the so-called 'umbral calculus' (which he also worked to rigorously formulate) to beautifully establish some combinatorial results. He's credited as setting the field of algebraic combinatorics on solid ground via his seminal papers On the Foundations of Combinatorial Theory. But it's not just the technical results -- his writing is just plain fun to read.
Given my personal interests, I really appreciate that although Rota did so much work in combinatorics he always seemed to lean back towards his roots in functional analysis & probability. In fact, his goal to find the true nature of classical results in analysis and probability led him to a great deal of good work in combinatorics, e.g. his work on the Rota-Baxter algebra inspired by his ambition to understand "the algebra of indefinite integration", and his work on the foundations of probability with the ambition to understand the middle ground between the discrete and the continuous. Moreso than most people he is willing to put his position out there and speak about mathematics rather than just speak mathematics. A great example of this is his book "Indiscrete Thoughts" -- definitely worth reading. You may not agree with many things he says but it's wonderful to be allowed a glimpse into the mind of a man such as Rota.